By Géza Schay
Building at the author's past version at the topic (Introduction toLinear Algebra, Jones & Bartlett, 1996), this booklet bargains a refreshingly concise textual content compatible for the standard direction in linear algebra, providing a delicately chosen array of crucial issues that may be completely lined in one semester. even supposing the exposition more often than not falls in response to the fabric suggested by way of the Linear Algebra Curriculum examine workforce, it significantly deviates in delivering an early emphasis at the geometric foundations of linear algebra. this offers scholars a extra intuitive knowing of the topic and allows a neater grab of extra summary innovations lined later within the path.
The concentration all through is rooted within the mathematical basics, however the textual content additionally investigates a few fascinating functions, together with a bit on special effects, a bankruptcy on numerical tools, and lots of workouts and examples utilizing MATLAB. in the meantime, many visuals and difficulties (a whole options guide is accessible to teachers) are integrated to reinforce and toughen realizing in the course of the ebook.
Brief but particular and rigorous, this paintings is a perfect selection for a one-semester path in linear algebra designated basically at math or physics majors. it's a beneficial software for any professor who teaches the subject.
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Additional info for A Concise Introduction to Linear Algebra
B. When do we have equality in Part (a)? Explain! 15. Let p be any nonzero vector in R2 and up the unit vector in its direction. Show a. that the vector p can be written as p = |p|(cos φ, sin φ), where φ is the angle from the positive x-axis to p, and b. that up = (cos φ, sin φ). 16. Let p be any nonzero vector in R3 and up the unit vector in its direction. Show that a. the components up · i, up · j, up · k of up equal the cosines of the angles α1 , α2 , α3 between p and the positive coordinate axes (these are called the direction cosines of p), b.
This will turn out to be a very important and useful property. As we can see, the scalar product results in a scalar, which explains its ﬁrst name, as opposed to other products to be deﬁned later. As for the second name, we generally denote this product by a dot. The scalar product has some simple properties. 2. (Properties of the Dot Product). For all vectors p, q and r in Rn for any n and for every scalar c we have 1. p · q = q · p, 2. p · (q + r) = p · q + p · r, 3. c(p · q) = (cp) · q = p · (cq), and 2 4.
In the next six exercises ﬁnd the distances. 26. Between the point P0 (1, −2, 4) and the plane 3x + 2y − 2z = 3. 27. Between the point P0 (3, 4, 0) and the plane y − 2z = 5. 28. Between the lines p = (3, −2, 6) + s(−3, 5, 7) and p = (5, 1, 1) + t(−2, 1, 6). 29. Between the lines p = (2, 1, 5) + s(−4, 0, 3) and p = (0, −2, 3) + t(5, 0, −2). 30. Between the point P0 (3, 4, 0) and the line L : p = (3, −2, 6) + s(−3, 5, 7). 31. Between the point P0 (1, −2, 4) and the line p = (3, 2, −4) + s(7, −5, 4).